Engineering ultrastrong coupling between Josephson plasmon polaritons and subwavelength microcavity arrays in silicon/van der Waals layered superconductor heterostructure for terahertz hybrid circuit cavity quantum electrodynamics

The realization of the ultrastrong coupling between Josephson plasma waves (JPWs) and terahertz (THz) photons in subwavelength microcavity array is interest for manipulating THz cavity quantum electrodynamics (cQED), ultrahigh-resolution sensing imaging, information processing. Here, we describe engineering light-matter interactions a deeply based on hybrid silicon high-temperature superconductor (HTS) ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}\mathrm{Ca}{\mathrm{Cu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ (BSCCO) van der Waals (vdW) heterostructure. We perform numerical modeling analytical calculation to cQED process radiation JPWs medium which naturally present BSCCO vdW. resonance frequency microcavities swept through by altering their width. reflection demonstrates anticrossing behavior with normalized Rabi (coupling strength) $2{\mathrm{\ensuremath{\Omega}}}_{\mathrm{R}}/{f}_{\mathrm{c}}=0.29$ thickness $t=200$ nm, increases value 0.87 $t=800$ nm. Furthermore, thermal strength shows modulation splitting $2{\mathrm{\ensuremath{\Omega}}}_{\mathrm{R}}$ temperature. show that $2{\mathrm{\ensuremath{\Omega}}}_{\mathrm{R}}/{f}_{\mathrm{c}}$ independent temperature superconducting regime, while weak can be observed above transition proposed chip-scale photonic integrated circuit metamaterial shall guide effort development power-efficient coherent sources, sensors, ultrasensitive detectors, parametric amplifiers tunable bolometers HTS material.